Question

graph the following function. give the x- and y-intercepts. f(x)=√(x + 4) - 4 find x axis intercept find y axis intercept

Explanation:

Find X - axis intercept

Step 1: Set \( f(x) = 0 \)

To find the x - intercept, we know that on the x - axis, the value of \( y=f(x) \) is 0. So we set up the equation \( 0=\sqrt{x + 4}-4 \).

Step 2: Solve for \( x \)

First, add 4 to both sides of the equation: \( \sqrt{x + 4}=4 \). Then, square both sides of the equation to get rid of the square root: \( x + 4=4^{2}=16 \). Finally, subtract 4 from both sides: \( x=16 - 4=12 \).

Step 1: Set \( x = 0 \)

To find the y - intercept, we know that on the y - axis, the value of \( x \) is 0. So we substitute \( x = 0 \) into the function \( f(x)=\sqrt{x + 4}-4 \).

Step 2: Calculate \( f(0) \)

\( f(0)=\sqrt{0 + 4}-4=\sqrt{4}-4 = 2-4=-2 \).

Answer:

The x - intercept is \( x = 12 \) (the point is \( (12,0) \))

Find Y - axis intercept